Statistics 4220 Test 1
NAME: _________________________________________
Instructions:
Read these instructions
Do not turn the page until the test begins
You have 50 minutes
This test is printed on both sides, so don’t miss a page.
Each question is worth double the number of minutes. This test is timed for 50 minutes.
For this test you may use a page of notes, a calculator, z-tables
If you need any of these please find a solution before the exam begins
If you have a question during the test please come forward quietly so that you are not
disruptive. If you leave early please do so quietly. Note that I cannot give answers that
are part of the test, only clarify the English being used.
You must show your work. Answers which are correct but do not show any work may
not get full credit. I might assume you either guessed, cheated, or used some fancy
calculator.
Cheating is not tolerated. Any inappropriate activity will be discussed after the final
Hats or hoods must be moved so that your face is not obscured.
Please turn off your cell phone. You cannot have your phone out at all.
No one wants to hear “Love me love me say that you love me” during the test.
The waiting time until you have three cars on the Clark Street Bridge at the same time is gamma
distributed with an average of 22 minutes and a standard deviation of 52 minutes. This is important
because there are concerns as to whether a concrete bridge can hold three cars at the same time. A
team of engineers is going to monitor the bridge situation by randomly selecting 250 times to watch the
bridge and recording how long they had to wait until there were three cars at the same time. Their
results showed an average of 19 minutes and a standard deviation of 37 minutes. Because of their
report the Laramie city council is now debating whether to rebuild the bridge from iron.
(4 minutes)
1) There are 5 numbers in the scenario above (written in numerical form – the “three” doesn’t count)
For each determine whether it is a Statistic or Parameter, and write the correct symbol for it (e.g. β=61)
STATISTIC
PARAMETER
_
(2 minutes)
2) Using the scenario of the Clark Street Bridge above, if a new study of 250 random times was
observed, what is the probability of getting an average of 19 minutes?
(8 minutes)
3) The number of cracks in a concrete bridge can be as high as 5 cracks (after that it will collapse). For
randomly selected bridges across the US, the distribution of cracks in concrete bridges is shown
below:
Cracks
f(x)
0
0.03
1
0.07
2
0.10
3
0.20
4
0.50
What is the standard deviation for the number of cracks in a concrete bridge?
5
0.10
(2 minutes)
4) A sample of 400 computers measured the heat on the motherboard. The boxplot for the data is
shown below. Select the histogram that matches the boxplot
(8 minutes)
5) The speed of an arrow is N(240, 102) fps. To get consistent grouping on a target the arrow is
supposed to fly at a speed between 227.7 and 271.4 fps (too slow and the wind will be a problem,
too fast and the tension on the bow is too great). What is the probability a random arrow will
qualify as consistent?
(2 minutes)
6) The distribution for salaries of civil engineers in California has a mean of $75 K/year and a standard
deviation of $15 K/year. The UC Berkeley engineering department randomly selects 10 engineers to
come speak at convocation. What is the probability the average of their salaries will be more than
$150 K/year?
(6 minutes)
7) It was requested that I use f(x)=x2 as the function for this test. However, that needs bounds and it
needs to be scaled so that the distribution is a valid pdf. I will restrict x to be greater than zero, but I
want you to give the other values. Make this a valid pdf (there is more than one correct answer)
In other words:
f(x) = k x2
for
0<x<a
k=
a=
(8 minutes)
8) The military will test the new RUANME sniper bullet by firing from a rooftop at a target 800 meters
away from the sniper. The distribution for where the bullet actually hits is N(800, 502) meters away
from the sniper (in the direction of the target). Reporters would like to lie down as close to the
target as they are allowed (and of course in the line of fire). Your job is to define a safe distance
such that there is only a 1% chance that any reporter will get hit by the bullet.
(6 minutes)
9) The time it takes a square foot of paint to dry is distributed N(16, 9) hours. A team of history majors
is recruited to watch 25 random square feet of paint, and they will average the amount of time it
took each square foot to dry. What is the probability their average will be less than 18 hours?
(3 minutes)
10) The force on a seat belt during a car crash is distributed as highly right skewed with a mean of 110 N
and a standard deviation of 54 N. A random sample of 81 car crashes is simulated. The goal is to
find the probability of getting an average force from this sample of 119 N or more. Answer this
question by shading in the area on the normal curve shown that matches the probability asked for.
(1 minute)
11) If there was a big party, how would you be able to pick the engineers out of the group?